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Simplifying x(x + -5) + 1 = 3x(x + 3) Reorder the terms: x(-5 + x) + 1 = 3x(x + 3) (-5 * x + x * x) + 1 = 3x(x + 3) (-5x + x2) + 1 = 3x(x + 3) Reorder the terms: 1 + -5x + x2 = 3x(x + 3) Reorder the terms: 1 + -5x + x2 = 3x(3 + x) 1 + -5x + x2 = (3 * 3x + x * 3x) 1 + -5x + x2 = (9x + 3x2) Solving 1 + -5x + x2 = 9x + 3x2 Solving for variable 'x'. Reorder the terms: 1 + -5x + -9x + x2 + -3x2 = 9x + 3x2 + -9x + -3x2 Combine like terms: -5x + -9x = -14x 1 + -14x + x2 + -3x2 = 9x + 3x2 + -9x + -3x2 Combine like terms: x2 + -3x2 = -2x2 1 + -14x + -2x2 = 9x + 3x2 + -9x + -3x2 Reorder the terms: 1 + -14x + -2x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 1 + -14x + -2x2 = 0 + 3x2 + -3x2 1 + -14x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 1 + -14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 7x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 7x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 7x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 7x + x2 = 0 + 0.5 7x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 7x + x2 = 0.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 0.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 0.5 + 12.25 Combine like terms: 0.5 + 12.25 = 12.75 12.25 + 7x + x2 = 12.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 3.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 3.5 = 3.570714214 Simplifying x + 3.5 = 3.570714214 Reorder the terms: 3.5 + x = 3.570714214 Solving 3.5 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.570714214 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.570714214 + -3.5 x = 3.570714214 + -3.5 Combine like terms: 3.570714214 + -3.5 = 0.070714214 x = 0.070714214 Simplifying x = 0.070714214Subproblem 2
x + 3.5 = -3.570714214 Simplifying x + 3.5 = -3.570714214 Reorder the terms: 3.5 + x = -3.570714214 Solving 3.5 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.570714214 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.570714214 + -3.5 x = -3.570714214 + -3.5 Combine like terms: -3.570714214 + -3.5 = -7.070714214 x = -7.070714214 Simplifying x = -7.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.070714214, -7.070714214}
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